In a force balanced motion sensor instrument, such as an accelerometer for example, it is generally desired that the instrument output signal be proportional to the input condition to be sensed. Therefore, in many types of electrostatic and electromagnetic force balanced sensing instruments special techniques are required to obtain a linear relation between the instrument output and the sensed input. In electrostatic and electromagnetic instruments, the forces applied by the instrument forcer are not linearly related to the feedback voltage or current supplied to the forcer. Furthermore, for optimum operation of the instrument itself, it is preferred that the feedback force applied by the feedback control network have a linear relation to the sensed input. Thus, special techniques have been employed for obtaining such linearity.
For example, in an electrostatic force balanced accelerometer, electrostatic forcing in a closed loop system is employed to position and obtain an output from a pendulous inertial mass or proof mass. The electrostatic forcing system employs a capacitive pickoff electrode on each side of a pendulous member that has been etched from a silicon substrate. A control pulse is employed to sequentially apply a constant amount of charge to each electrode. A variable force is applied to the inertial mass by varying the amount of time (e.g., duty cycle) the charge is left on a respective structure. The amount of time the charge is left on a respective structure is based on the displacement of the inertial mass relative to a null position. This type of forcing system generally requires the use of sample and hold circuits followed by comparator error amplifiers to measure the charge left on the respective structures. Also, the control pulse should be left on the structure for a substantial period of time to enable proper sampling which can in turn wear down the effectiveness of the accelerometer over time.